LMFDB - Embedded newform 4020.2.q.l.841.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.6
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.l.3781.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} -1.00000 q^{5} +(0.278615 - 0.482575i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} -1.00000 q^{5} +(0.278615 - 0.482575i) q^{7} +1.00000 q^{9} +(-0.747022 + 1.29388i) q^{11} +(-1.66587 - 2.88537i) q^{13} +1.00000 q^{15} +(-3.16705 - 5.48549i) q^{17} +(-2.84562 - 4.92876i) q^{19} +(-0.278615 + 0.482575i) q^{21} +(2.62889 + 4.55337i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-1.03441 + 1.79165i) q^{29} +(-3.14873 + 5.45376i) q^{31} +(0.747022 - 1.29388i) q^{33} +(-0.278615 + 0.482575i) q^{35} +(4.16330 + 7.21105i) q^{37} +(1.66587 + 2.88537i) q^{39} +(3.52430 - 6.10426i) q^{41} -10.7357 q^{43} -1.00000 q^{45} +(3.75522 - 6.50424i) q^{47} +(3.34475 + 5.79327i) q^{49} +(3.16705 + 5.48549i) q^{51} +0.994479 q^{53} +(0.747022 - 1.29388i) q^{55} +(2.84562 + 4.92876i) q^{57} +13.7751 q^{59} +(-1.32946 - 2.30269i) q^{61} +(0.278615 - 0.482575i) q^{63} +(1.66587 + 2.88537i) q^{65} +(4.44952 + 6.87035i) q^{67} +(-2.62889 - 4.55337i) q^{69} +(1.28175 - 2.22006i) q^{71} +(-6.29556 - 10.9042i) q^{73} -1.00000 q^{75} +(0.416263 + 0.720988i) q^{77} +(-4.62898 + 8.01762i) q^{79} +1.00000 q^{81} +(-1.13476 - 1.96546i) q^{83} +(3.16705 + 5.48549i) q^{85} +(1.03441 - 1.79165i) q^{87} -4.78115 q^{89} -1.85654 q^{91} +(3.14873 - 5.45376i) q^{93} +(2.84562 + 4.92876i) q^{95} +(3.17186 + 5.49382i) q^{97} +(-0.747022 + 1.29388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	$ 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) $ 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	0.278615	−	0.482575i	0.105306	−	0.182396i	−0.808557	−	0.588418i	$-0.799751\pi$
$7$	0.278615	−	0.482575i	0.105306	−	0.182396i	0.913863	+	0.406022i	$0.133084\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.747022	+	1.29388i	−0.225236	+	0.390120i	−0.956390	−	0.292092i	$-0.905649\pi$
$11$	−0.747022	+	1.29388i	−0.225236	+	0.390120i	0.731154	+	0.682212i	$0.238982\pi$
$12$		0			0
$13$	−1.66587	−	2.88537i	−0.462029	−	0.800258i	0.537033	−	0.843562i	$-0.319545\pi$
$13$	−1.66587	−	2.88537i	−0.462029	−	0.800258i	−0.999062	+	0.0433031i	$0.986212\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−3.16705	−	5.48549i	−0.768122	−	1.33043i	−0.938580	−	0.345061i	$-0.887858\pi$
$17$	−3.16705	−	5.48549i	−0.768122	−	1.33043i	0.170458	−	0.985365i	$-0.445475\pi$
$18$		0			0
$19$	−2.84562	−	4.92876i	−0.652830	−	1.13074i	−0.982433	−	0.186616i	$-0.940248\pi$
$19$	−2.84562	−	4.92876i	−0.652830	−	1.13074i	0.329603	−	0.944120i	$-0.393085\pi$
$20$		0			0
$21$	−0.278615	+	0.482575i	−0.0607987	+	0.105306i
$22$		0			0
$23$	2.62889	+	4.55337i	0.548161	+	0.949443i	0.998401	+	0.0565354i	$0.0180054\pi$
$23$	2.62889	+	4.55337i	0.548161	+	0.949443i	−0.450239	+	0.892908i	$0.648661\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.03441	+	1.79165i	−0.192085	+	0.332702i	−0.945941	−	0.324338i	$-0.894858\pi$
$29$	−1.03441	+	1.79165i	−0.192085	+	0.332702i	0.753856	+	0.657040i	$0.228192\pi$
$30$		0			0
$31$	−3.14873	+	5.45376i	−0.565528	+	0.979524i	0.431472	+	0.902126i	$0.357994\pi$
$31$	−3.14873	+	5.45376i	−0.565528	+	0.979524i	−0.997000	+	0.0773974i	$0.975339\pi$
$32$		0			0
$33$	0.747022	−	1.29388i	0.130040	−	0.225236i
$34$		0			0
$35$	−0.278615	+	0.482575i	−0.0470944	+	0.0815700i
$36$		0			0
$37$	4.16330	+	7.21105i	0.684443	+	1.18549i	0.973612	+	0.228211i	$0.0732877\pi$
$37$	4.16330	+	7.21105i	0.684443	+	1.18549i	−0.289169	+	0.957278i	$0.593379\pi$
$38$		0			0
$39$	1.66587	+	2.88537i	0.266753	+	0.462029i
$40$		0			0
$41$	3.52430	−	6.10426i	0.550403	−	0.953326i	−0.447843	−	0.894112i	$-0.647807\pi$
$41$	3.52430	−	6.10426i	0.550403	−	0.953326i	0.998245	−	0.0592132i	$-0.0188592\pi$
$42$		0			0
$43$	−10.7357			−1.63718			−0.818592	−	0.574375i	$-0.805245\pi$
$43$	−10.7357			−1.63718			−0.818592	+	0.574375i	$0.805245\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	3.75522	−	6.50424i	0.547756	−	0.948741i	−0.450672	−	0.892689i	$-0.648816\pi$
$47$	3.75522	−	6.50424i	0.547756	−	0.948741i	0.998428	−	0.0560511i	$-0.0178510\pi$
$48$		0			0
$49$	3.34475	+	5.79327i	0.477821	+	0.827610i
$50$		0			0
$51$	3.16705	+	5.48549i	0.443475	+	0.768122i
$52$		0			0
$53$	0.994479			0.136602			0.0683011	−	0.997665i	$-0.478242\pi$
$53$	0.994479			0.136602			0.0683011	+	0.997665i	$0.478242\pi$
$54$		0			0
$55$	0.747022	−	1.29388i	0.100728	−	0.174467i
$56$		0			0
$57$	2.84562	+	4.92876i	0.376912	+	0.652830i
$58$		0			0
$59$	13.7751			1.79336			0.896680	−	0.442680i	$-0.145972\pi$
$59$	13.7751			1.79336			0.896680	+	0.442680i	$0.145972\pi$
$60$		0			0
$61$	−1.32946	−	2.30269i	−0.170220	−	0.294830i	0.768277	−	0.640118i	$-0.221114\pi$
$61$	−1.32946	−	2.30269i	−0.170220	−	0.294830i	−0.938497	+	0.345288i	$0.887781\pi$
$62$		0			0
$63$	0.278615	−	0.482575i	0.0351021	−	0.0607987i
$64$		0			0
$65$	1.66587	+	2.88537i	0.206626	+	0.357886i
$66$		0			0
$67$	4.44952	+	6.87035i	0.543595	+	0.839347i
$67$	4.44952	+	6.87035i	0.543595	+	0.839347i
$68$		0			0
$69$	−2.62889	−	4.55337i	−0.316481	−	0.548161i
$70$		0			0
$71$	1.28175	−	2.22006i	0.152116	−	0.263473i	−0.779889	−	0.625918i	$-0.784725\pi$
$71$	1.28175	−	2.22006i	0.152116	−	0.263473i	0.932005	+	0.362445i	$0.118058\pi$
$72$		0			0
$73$	−6.29556	−	10.9042i	−0.736840	−	1.27624i	−0.953911	−	0.300089i	$-0.902984\pi$
$73$	−6.29556	−	10.9042i	−0.736840	−	1.27624i	0.217071	−	0.976156i	$-0.430350\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	0.416263	+	0.720988i	0.0474375	+	0.0821642i
$78$		0			0
$79$	−4.62898	+	8.01762i	−0.520801	+	0.902053i	0.478907	+	0.877866i	$0.341033\pi$
$79$	−4.62898	+	8.01762i	−0.520801	+	0.902053i	−0.999707	+	0.0241874i	$0.992300\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−1.13476	−	1.96546i	−0.124556	−	0.215738i	0.797003	−	0.603975i	$-0.206417\pi$
$83$	−1.13476	−	1.96546i	−0.124556	−	0.215738i	−0.921559	+	0.388237i	$0.873084\pi$
$84$		0			0
$85$	3.16705	+	5.48549i	0.343515	+	0.594985i
$86$		0			0
$87$	1.03441	−	1.79165i	0.110901	−	0.192085i
$88$		0			0
$89$	−4.78115			−0.506801			−0.253401	−	0.967361i	$-0.581549\pi$
$89$	−4.78115			−0.506801			−0.253401	+	0.967361i	$0.581549\pi$
$90$		0			0
$91$	−1.85654			−0.194619
$92$		0			0
$93$	3.14873	−	5.45376i	0.326508	−	0.565528i
$94$		0			0
$95$	2.84562	+	4.92876i	0.291955	+	0.505680i
$96$		0			0
$97$	3.17186	+	5.49382i	0.322054	+	0.557813i	0.980912	−	0.194454i	$-0.0622935\pi$
$97$	3.17186	+	5.49382i	0.322054	+	0.557813i	−0.658858	+	0.752267i	$0.728960\pi$
$98$		0			0
$99$	−0.747022	+	1.29388i	−0.0750786	+	0.130040i
$100$		0			0
$101$	−5.77102	+	9.99569i	−0.574237	+	0.994609i	0.421887	+	0.906649i	$0.361368\pi$
$101$	−5.77102	+	9.99569i	−0.574237	+	0.994609i	−0.996124	+	0.0879599i	$0.971965\pi$
$102$		0			0
$103$	−5.46368	+	9.46337i	−0.538352	+	0.932454i	0.460641	+	0.887587i	$0.347620\pi$
$103$	−5.46368	+	9.46337i	−0.538352	+	0.932454i	−0.998993	+	0.0448670i	$0.985714\pi$
$104$		0			0
$105$	0.278615	−	0.482575i	0.0271900	−	0.0470944i
$106$		0			0
$107$	−12.5291			−1.21124			−0.605618	−	0.795756i	$-0.707074\pi$
$107$	−12.5291			−1.21124			−0.605618	+	0.795756i	$0.707074\pi$
$108$		0			0
$109$	−0.395687			−0.0378999			−0.0189500	−	0.999820i	$-0.506032\pi$
$109$	−0.395687			−0.0378999			−0.0189500	+	0.999820i	$0.506032\pi$
$110$		0			0
$111$	−4.16330	−	7.21105i	−0.395163	−	0.684443i
$112$		0			0
$113$	1.58814	−	2.75075i	0.149400	−	0.258769i	−0.781606	−	0.623773i	$-0.785599\pi$
$113$	1.58814	−	2.75075i	0.149400	−	0.258769i	0.931006	+	0.365004i	$0.118932\pi$
$114$		0			0
$115$	−2.62889	−	4.55337i	−0.245145	−	0.424604i
$116$		0			0
$117$	−1.66587	−	2.88537i	−0.154010	−	0.266753i
$118$		0			0
$119$	−3.52954			−0.323553
$120$		0			0
$121$	4.38392	+	7.59316i	0.398538	+	0.690288i
$122$		0			0
$123$	−3.52430	+	6.10426i	−0.317775	+	0.550403i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	2.74734	−	4.75853i	0.243787	−	0.422251i	−0.718003	−	0.696040i	$-0.754944\pi$
$127$	2.74734	−	4.75853i	0.243787	−	0.422251i	0.961790	+	0.273789i	$0.0882769\pi$
$128$		0			0
$129$	10.7357			0.945229
$130$		0			0
$131$	1.21891			0.106497			0.0532483	−	0.998581i	$-0.483043\pi$
$131$	1.21891			0.106497			0.0532483	+	0.998581i	$0.483043\pi$
$132$		0			0
$133$	−3.17133			−0.274989
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−18.0492			−1.54205			−0.771024	−	0.636806i	$-0.780255\pi$
$137$	−18.0492			−1.54205			−0.771024	+	0.636806i	$0.780255\pi$
$138$		0			0
$139$	−6.41888			−0.544442			−0.272221	−	0.962235i	$-0.587758\pi$
$139$	−6.41888			−0.544442			−0.272221	+	0.962235i	$0.587758\pi$
$140$		0			0
$141$	−3.75522	+	6.50424i	−0.316247	+	0.547756i
$142$		0			0
$143$	4.97777			0.416262
$144$		0			0
$145$	1.03441	−	1.79165i	0.0859032	−	0.148789i
$146$		0			0
$147$	−3.34475	−	5.79327i	−0.275870	−	0.477821i
$148$		0			0
$149$	−18.4943			−1.51511			−0.757556	−	0.652770i	$-0.773607\pi$
$149$	−18.4943			−1.51511			−0.757556	+	0.652770i	$0.773607\pi$
$150$		0			0
$151$	10.2407	+	17.7374i	0.833374	+	1.44345i	0.895348	+	0.445368i	$0.146927\pi$
$151$	10.2407	+	17.7374i	0.833374	+	1.44345i	−0.0619743	+	0.998078i	$0.519740\pi$
$152$		0			0
$153$	−3.16705	−	5.48549i	−0.256041	−	0.443475i
$154$		0			0
$155$	3.14873	−	5.45376i	0.252912	−	0.438056i
$156$		0			0
$157$	4.06938	+	7.04837i	0.324772	+	0.562521i	0.981466	−	0.191636i	$-0.0613792\pi$
$157$	4.06938	+	7.04837i	0.324772	+	0.562521i	−0.656694	+	0.754157i	$0.728046\pi$
$158$		0			0
$159$	−0.994479			−0.0788673
$160$		0			0
$161$	2.92979			0.230900
$162$		0			0
$163$	−2.81656	+	4.87843i	−0.220610	+	0.382108i	−0.954993	−	0.296627i	$-0.904138\pi$
$163$	−2.81656	+	4.87843i	−0.220610	+	0.382108i	0.734383	+	0.678735i	$0.237472\pi$
$164$		0			0
$165$	−0.747022	+	1.29388i	−0.0581556	+	0.100728i
$166$		0			0
$167$	6.27155	−	10.8626i	0.485307	−	0.840576i	−0.514550	−	0.857460i	$-0.672041\pi$
$167$	6.27155	−	10.8626i	0.485307	−	0.840576i	0.999857	+	0.0168837i	$0.00537450\pi$
$168$		0			0
$169$	0.949749	−	1.64501i	0.0730576	−	0.126540i
$170$		0			0
$171$	−2.84562	−	4.92876i	−0.217610	−	0.376912i
$172$		0			0
$173$	5.39925	+	9.35177i	0.410497	+	0.711002i	0.994944	−	0.100430i	$-0.0320219\pi$
$173$	5.39925	+	9.35177i	0.410497	+	0.711002i	−0.584447	+	0.811432i	$0.698689\pi$
$174$		0			0
$175$	0.278615	−	0.482575i	0.0210613	−	0.0364792i
$176$		0			0
$177$	−13.7751			−1.03540
$178$		0			0
$179$	2.17443			0.162524			0.0812622	−	0.996693i	$-0.474105\pi$
$179$	2.17443			0.162524			0.0812622	+	0.996693i	$0.474105\pi$
$180$		0			0
$181$	−12.4845	+	21.6238i	−0.927966	+	1.60728i	−0.141245	+	0.989975i	$0.545111\pi$
$181$	−12.4845	+	21.6238i	−0.927966	+	1.60728i	−0.786721	+	0.617309i	$0.788223\pi$
$182$		0			0
$183$	1.32946	+	2.30269i	0.0982765	+	0.170220i
$184$		0			0
$185$	−4.16330	−	7.21105i	−0.306092	−	0.530167i
$186$		0			0
$187$	9.46342			0.692034
$188$		0			0
$189$	−0.278615	+	0.482575i	−0.0202662	+	0.0351021i
$190$		0			0
$191$	12.9393	+	22.4116i	0.936257	+	1.62164i	0.772378	+	0.635163i	$0.219067\pi$
$191$	12.9393	+	22.4116i	0.936257	+	1.62164i	0.163879	+	0.986480i	$0.447599\pi$
$192$		0			0
$193$	21.4833			1.54640			0.773201	−	0.634161i	$-0.218654\pi$
$193$	21.4833			1.54640			0.773201	+	0.634161i	$0.218654\pi$
$194$		0			0
$195$	−1.66587	−	2.88537i	−0.119295	−	0.206626i
$196$		0			0
$197$	−2.02629	+	3.50963i	−0.144367	+	0.250051i	−0.929137	−	0.369737i	$-0.879448\pi$
$197$	−2.02629	+	3.50963i	−0.144367	+	0.250051i	0.784770	+	0.619788i	$0.212781\pi$
$198$		0			0
$199$	10.4217	+	18.0509i	0.738772	+	1.27959i	0.953048	+	0.302818i	$0.0979274\pi$
$199$	10.4217	+	18.0509i	0.738772	+	1.27959i	−0.214276	+	0.976773i	$0.568739\pi$
$200$		0			0
$201$	−4.44952	−	6.87035i	−0.313845	−	0.484597i
$202$		0			0
$203$	0.576404	+	0.998361i	0.0404556	+	0.0700712i
$204$		0			0
$205$	−3.52430	+	6.10426i	−0.246148	+	0.426340i
$206$		0			0
$207$	2.62889	+	4.55337i	0.182720	+	0.316481i
$208$		0			0
$209$	8.50297			0.588163
$210$		0			0
$211$	12.5884	+	21.8038i	0.866622	+	1.50103i	0.865428	+	0.501034i	$0.167047\pi$
$211$	12.5884	+	21.8038i	0.866622	+	1.50103i	0.00119422	+	0.999999i	$0.499620\pi$
$212$		0			0
$213$	−1.28175	+	2.22006i	−0.0878244	+	0.152116i
$214$		0			0
$215$	10.7357			0.732171
$216$		0			0
$217$	1.75456	+	3.03899i	0.119107	+	0.206300i
$218$		0			0
$219$	6.29556	+	10.9042i	0.425415	+	0.736840i
$220$		0			0
$221$	−10.5518	+	18.2762i	−0.709790	+	1.22939i
$222$		0			0
$223$	15.0596			1.00847			0.504234	−	0.863567i	$-0.331775\pi$
$223$	15.0596			1.00847			0.504234	+	0.863567i	$0.331775\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−0.542579	+	0.939775i	−0.0360122	+	0.0623750i	−0.883470	−	0.468488i	$-0.844799\pi$
$227$	−0.542579	+	0.939775i	−0.0360122	+	0.0623750i	0.847458	+	0.530863i	$0.178132\pi$
$228$		0			0
$229$	−2.45444	−	4.25122i	−0.162194	−	0.280929i	0.773461	−	0.633844i	$-0.218524\pi$
$229$	−2.45444	−	4.25122i	−0.162194	−	0.280929i	−0.935655	+	0.352915i	$0.885190\pi$
$230$		0			0
$231$	−0.416263	−	0.720988i	−0.0273881	−	0.0474375i
$232$		0			0
$233$	−2.29817	+	3.98055i	−0.150558	+	0.260774i	−0.931433	−	0.363913i	$-0.881440\pi$
$233$	−2.29817	+	3.98055i	−0.150558	+	0.260774i	0.780875	+	0.624688i	$0.214774\pi$
$234$		0			0
$235$	−3.75522	+	6.50424i	−0.244964	+	0.424290i
$236$		0			0
$237$	4.62898	−	8.01762i	0.300684	−	0.520801i
$238$		0			0
$239$	1.37954	−	2.38943i	0.0892350	−	0.154560i	−0.817953	−	0.575285i	$-0.804891\pi$
$239$	1.37954	−	2.38943i	0.0892350	−	0.154560i	0.907188	+	0.420725i	$0.138224\pi$
$240$		0			0
$241$	−26.7135			−1.72077			−0.860384	−	0.509647i	$-0.829776\pi$
$241$	−26.7135			−1.72077			−0.860384	+	0.509647i	$0.829776\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−3.34475	−	5.79327i	−0.213688	−	0.370119i
$246$		0			0
$247$	−9.48088	+	16.4214i	−0.603254	+	1.04487i
$248$		0			0
$249$	1.13476	+	1.96546i	0.0719125	+	0.124556i
$250$		0			0
$251$	13.6609	+	23.6614i	0.862269	+	1.49349i	0.869734	+	0.493521i	$0.164290\pi$
$251$	13.6609	+	23.6614i	0.862269	+	1.49349i	−0.00746532	+	0.999972i	$0.502376\pi$
$252$		0			0
$253$	−7.85536			−0.493862
$254$		0			0
$255$	−3.16705	−	5.48549i	−0.198328	−	0.343515i
$256$		0			0
$257$	8.27080	−	14.3255i	0.515919	−	0.893597i	−0.483911	−	0.875117i	$-0.660784\pi$
$257$	8.27080	−	14.3255i	0.515919	−	0.893597i	0.999829	−	0.0184797i	$-0.00588260\pi$
$258$		0			0
$259$	4.63982			0.288305
$260$		0			0
$261$	−1.03441	+	1.79165i	−0.0640285	+	0.110901i
$262$		0			0
$263$	5.76571			0.355529			0.177764	−	0.984073i	$-0.443113\pi$
$263$	5.76571			0.355529			0.177764	+	0.984073i	$0.443113\pi$
$264$		0			0
$265$	−0.994479			−0.0610904
$266$		0			0
$267$	4.78115			0.292602
$268$		0			0
$269$	−14.2969			−0.871698			−0.435849	−	0.900020i	$-0.643552\pi$
$269$	−14.2969			−0.871698			−0.435849	+	0.900020i	$0.643552\pi$
$270$		0			0
$271$	13.7819			0.837189			0.418595	−	0.908173i	$-0.362523\pi$
$271$	13.7819			0.837189			0.418595	+	0.908173i	$0.362523\pi$
$272$		0			0
$273$	1.85654			0.112363
$274$		0			0
$275$	−0.747022	+	1.29388i	−0.0450471	+	0.0780239i
$276$		0			0
$277$	−22.6410			−1.36037			−0.680183	−	0.733042i	$-0.738100\pi$
$277$	−22.6410			−1.36037			−0.680183	+	0.733042i	$0.738100\pi$
$278$		0			0
$279$	−3.14873	+	5.45376i	−0.188509	+	0.326508i
$280$		0			0
$281$	−1.05658	−	1.83005i	−0.0630302	−	0.109171i	0.832788	−	0.553592i	$-0.186743\pi$
$281$	−1.05658	−	1.83005i	−0.0630302	−	0.109171i	−0.895819	+	0.444420i	$0.853410\pi$
$282$		0			0
$283$	−5.03860			−0.299514			−0.149757	−	0.988723i	$-0.547849\pi$
$283$	−5.03860			−0.299514			−0.149757	+	0.988723i	$0.547849\pi$
$284$		0			0
$285$	−2.84562	−	4.92876i	−0.168560	−	0.291955i
$286$		0			0
$287$	−1.96384	−	3.40147i	−0.115922	−	0.200783i
$288$		0			0
$289$	−11.5604	+	20.0232i	−0.680023	+	1.17783i
$290$		0			0
$291$	−3.17186	−	5.49382i	−0.185938	−	0.322054i
$292$		0			0
$293$	17.3862			1.01572			0.507858	−	0.861441i	$-0.330438\pi$
$293$	17.3862			1.01572			0.507858	+	0.861441i	$0.330438\pi$
$294$		0			0
$295$	−13.7751			−0.802015
$296$		0			0
$297$	0.747022	−	1.29388i	0.0433466	−	0.0750786i
$298$		0			0
$299$	8.75878	−	15.1707i	0.506533	−	0.877342i
$300$		0			0
$301$	−2.99113	+	5.18079i	−0.172406	+	0.298616i
$302$		0			0
$303$	5.77102	−	9.99569i	0.331536	−	0.574237i
$304$		0			0
$305$	1.32946	+	2.30269i	0.0761247	+	0.131852i
$306$		0			0
$307$	−0.164247	−	0.284485i	−0.00937409	−	0.0162364i	0.861300	−	0.508096i	$-0.169651\pi$
$307$	−0.164247	−	0.284485i	−0.00937409	−	0.0162364i	−0.870674	+	0.491860i	$0.836317\pi$
$308$		0			0
$309$	5.46368	−	9.46337i	0.310818	−	0.538352i
$310$		0			0
$311$	−27.1554			−1.53984			−0.769920	−	0.638140i	$-0.779704\pi$
$311$	−27.1554			−1.53984			−0.769920	+	0.638140i	$0.779704\pi$
$312$		0			0
$313$	6.23667			0.352518			0.176259	−	0.984344i	$-0.443600\pi$
$313$	6.23667			0.352518			0.176259	+	0.984344i	$0.443600\pi$
$314$		0			0
$315$	−0.278615	+	0.482575i	−0.0156981	+	0.0271900i
$316$		0			0
$317$	11.8501	+	20.5249i	0.665567	+	1.15280i	0.979131	+	0.203229i	$0.0651434\pi$
$317$	11.8501	+	20.5249i	0.665567	+	1.15280i	−0.313565	+	0.949567i	$0.601523\pi$
$318$		0			0
$319$	−1.54546	−	2.67681i	−0.0865290	−	0.149873i
$320$		0			0
$321$	12.5291			0.699307
$322$		0			0
$323$	−18.0244	+	31.2193i	−1.00291	+	1.73709i
$324$		0			0
$325$	−1.66587	−	2.88537i	−0.0924059	−	0.160052i
$326$		0			0
$327$	0.395687			0.0218815
$328$		0			0
$329$	−2.09252	−	3.62435i	−0.115364	−	0.199817i
$330$		0			0
$331$	−5.92309	+	10.2591i	−0.325562	+	0.563891i	−0.981626	−	0.190815i	$-0.938887\pi$
$331$	−5.92309	+	10.2591i	−0.325562	+	0.563891i	0.656064	+	0.754706i	$0.272220\pi$
$332$		0			0
$333$	4.16330	+	7.21105i	0.228148	+	0.395163i
$334$		0			0
$335$	−4.44952	−	6.87035i	−0.243103	−	0.375368i
$336$		0			0
$337$	3.46795	+	6.00667i	0.188911	+	0.327204i	0.944888	−	0.327395i	$-0.106171\pi$
$337$	3.46795	+	6.00667i	0.188911	+	0.327204i	−0.755976	+	0.654599i	$0.772837\pi$
$338$		0			0
$339$	−1.58814	+	2.75075i	−0.0862562	+	0.149400i
$340$		0			0
$341$	−4.70434	−	8.14816i	−0.254754	−	0.441247i
$342$		0			0
$343$	7.62818			0.411883
$344$		0			0
$345$	2.62889	+	4.55337i	0.141535	+	0.245145i
$346$		0			0
$347$	−17.2518	+	29.8809i	−0.926123	+	1.60409i	−0.136378	+	0.990657i	$0.543546\pi$
$347$	−17.2518	+	29.8809i	−0.926123	+	1.60409i	−0.789745	+	0.613435i	$0.789787\pi$
$348$		0			0
$349$	−24.1538			−1.29292			−0.646461	−	0.762947i	$-0.723752\pi$
$349$	−24.1538			−1.29292			−0.646461	+	0.762947i	$0.723752\pi$
$350$		0			0
$351$	1.66587	+	2.88537i	0.0889176	+	0.154010i
$352$		0			0
$353$	−13.4956	−	23.3751i	−0.718298	−	1.24413i	−0.961674	−	0.274197i	$-0.911588\pi$
$353$	−13.4956	−	23.3751i	−0.718298	−	1.24413i	0.243376	−	0.969932i	$-0.421745\pi$
$354$		0			0
$355$	−1.28175	+	2.22006i	−0.0680285	+	0.117829i
$356$		0			0
$357$	3.52954			0.186803
$358$		0			0
$359$	31.8683			1.68194			0.840971	−	0.541080i	$-0.181984\pi$
$359$	31.8683			1.68194			0.840971	+	0.541080i	$0.181984\pi$
$360$		0			0
$361$	−6.69513	+	11.5963i	−0.352375	+	0.610332i
$362$		0			0
$363$	−4.38392	−	7.59316i	−0.230096	−	0.398538i
$364$		0			0
$365$	6.29556	+	10.9042i	0.329525	+	0.570754i
$366$		0			0
$367$	−10.9066	+	18.8908i	−0.569320	+	0.986091i	0.427313	+	0.904104i	$0.359460\pi$
$367$	−10.9066	+	18.8908i	−0.569320	+	0.986091i	−0.996633	+	0.0819875i	$0.973873\pi$
$368$		0			0
$369$	3.52430	−	6.10426i	0.183468	−	0.317775i
$370$		0			0
$371$	0.277076	−	0.479910i	0.0143851	−	0.0249157i
$372$		0			0
$373$	17.5733	−	30.4379i	0.909913	−	1.57601i	0.0957290	−	0.995407i	$-0.469482\pi$
$373$	17.5733	−	30.4379i	0.909913	−	1.57601i	0.814184	−	0.580607i	$-0.197185\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	6.89279			0.354997
$378$		0			0
$379$	−8.34665	−	14.4568i	−0.428739	−	0.742597i	0.568023	−	0.823013i	$-0.307709\pi$
$379$	−8.34665	−	14.4568i	−0.428739	−	0.742597i	−0.996761	+	0.0804158i	$0.974375\pi$
$380$		0			0
$381$	−2.74734	+	4.75853i	−0.140750	+	0.243787i
$382$		0			0
$383$	−18.1235	−	31.3908i	−0.926068	−	1.60400i	−0.789835	−	0.613319i	$-0.789834\pi$
$383$	−18.1235	−	31.3908i	−0.926068	−	1.60400i	−0.136232	−	0.990677i	$-0.543499\pi$
$384$		0			0
$385$	−0.416263	−	0.720988i	−0.0212147	−	0.0367449i
$386$		0			0
$387$	−10.7357			−0.545728
$388$		0			0
$389$	−13.8753	−	24.0327i	−0.703504	−	1.21850i	−0.967229	−	0.253907i	$-0.918284\pi$
$389$	−13.8753	−	24.0327i	−0.703504	−	1.21850i	0.263725	−	0.964598i	$-0.415049\pi$
$390$		0			0
$391$	16.6516	−	28.8415i	0.842110	−	1.45858i
$392$		0			0
$393$	−1.21891			−0.0614858
$394$		0			0
$395$	4.62898	−	8.01762i	0.232909	−	0.403410i
$396$		0			0
$397$	16.8265			0.844497			0.422249	−	0.906480i	$-0.361241\pi$
$397$	16.8265			0.844497			0.422249	+	0.906480i	$0.361241\pi$
$398$		0			0
$399$	3.17133			0.158765
$400$		0			0
$401$	−14.9026			−0.744202			−0.372101	−	0.928192i	$-0.621363\pi$
$401$	−14.9026			−0.744202			−0.372101	+	0.928192i	$0.621363\pi$
$402$		0			0
$403$	20.9815			1.04516
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−12.4403			−0.616644
$408$		0			0
$409$	−12.6606	+	21.9288i	−0.626027	+	1.08431i	0.362314	+	0.932056i	$0.381987\pi$
$409$	−12.6606	+	21.9288i	−0.626027	+	1.08431i	−0.988341	+	0.152255i	$0.951347\pi$
$410$		0			0
$411$	18.0492			0.890302
$412$		0			0
$413$	3.83793	−	6.64749i	0.188852	−	0.327102i
$414$		0			0
$415$	1.13476	+	1.96546i	0.0557032	+	0.0964808i
$416$		0			0
$417$	6.41888			0.314334
$418$		0			0
$419$	−8.95293	−	15.5069i	−0.437379	−	0.757563i	0.560107	−	0.828420i	$-0.310760\pi$
$419$	−8.95293	−	15.5069i	−0.437379	−	0.757563i	−0.997486	+	0.0708571i	$0.977427\pi$
$420$		0			0
$421$	−2.66283	−	4.61216i	−0.129778	−	0.224783i	0.793812	−	0.608163i	$-0.208093\pi$
$421$	−2.66283	−	4.61216i	−0.129778	−	0.224783i	−0.923591	+	0.383380i	$0.874760\pi$
$422$		0			0
$423$	3.75522	−	6.50424i	0.182585	−	0.316247i
$424$		0			0
$425$	−3.16705	−	5.48549i	−0.153624	−	0.266085i
$426$		0			0
$427$	−1.48163			−0.0717010
$428$		0			0
$429$	−4.97777			−0.240329
$430$		0			0
$431$	−6.07800	+	10.5274i	−0.292767	+	0.507087i	−0.974463	−	0.224548i	$-0.927909\pi$
$431$	−6.07800	+	10.5274i	−0.292767	+	0.507087i	0.681696	+	0.731636i	$0.261243\pi$
$432$		0			0
$433$	−17.5782	+	30.4463i	−0.844754	+	1.46316i	0.0410810	+	0.999156i	$0.486920\pi$
$433$	−17.5782	+	30.4463i	−0.844754	+	1.46316i	−0.885835	+	0.464001i	$0.846414\pi$
$434$		0			0
$435$	−1.03441	+	1.79165i	−0.0495962	+	0.0859032i
$436$		0			0
$437$	14.9617	−	25.9143i	0.715713	−	1.23965i
$438$		0			0
$439$	−2.83015	−	4.90197i	−0.135076	−	0.233958i	0.790551	−	0.612397i	$-0.209794\pi$
$439$	−2.83015	−	4.90197i	−0.135076	−	0.233958i	−0.925626	+	0.378439i	$0.876461\pi$
$440$		0			0
$441$	3.34475	+	5.79327i	0.159274	+	0.275870i
$442$		0			0
$443$	6.05312	−	10.4843i	0.287592	−	0.498124i	−0.685642	−	0.727939i	$-0.740479\pi$
$443$	6.05312	−	10.4843i	0.287592	−	0.498124i	0.973234	+	0.229814i	$0.0738119\pi$
$444$		0			0
$445$	4.78115			0.226648
$446$		0			0
$447$	18.4943			0.874751
$448$		0			0
$449$	−7.21283	+	12.4930i	−0.340394	+	0.589580i	−0.984506	−	0.175351i	$-0.943894\pi$
$449$	−7.21283	+	12.4930i	−0.340394	+	0.589580i	0.644112	+	0.764932i	$0.277227\pi$
$450$		0			0
$451$	5.26546	+	9.12004i	0.247941	+	0.429446i
$452$		0			0
$453$	−10.2407	−	17.7374i	−0.481148	−	0.833374i
$454$		0			0
$455$	1.85654			0.0870361
$456$		0			0
$457$	−2.73539	+	4.73784i	−0.127956	+	0.221627i	−0.922885	−	0.385076i	$-0.874175\pi$
$457$	−2.73539	+	4.73784i	−0.127956	+	0.221627i	0.794928	+	0.606703i	$0.207508\pi$
$458$		0			0
$459$	3.16705	+	5.48549i	0.147825	+	0.256041i
$460$		0			0
$461$	−26.4870			−1.23362			−0.616812	−	0.787110i	$-0.711576\pi$
$461$	−26.4870			−1.23362			−0.616812	+	0.787110i	$0.711576\pi$
$462$		0			0
$463$	−6.22418	−	10.7806i	−0.289262	−	0.501017i	0.684372	−	0.729133i	$-0.260077\pi$
$463$	−6.22418	−	10.7806i	−0.289262	−	0.501017i	−0.973634	+	0.228117i	$0.926743\pi$
$464$		0			0
$465$	−3.14873	+	5.45376i	−0.146019	+	0.252912i
$466$		0			0
$467$	15.7553	+	27.2891i	0.729071	+	1.26279i	0.957276	+	0.289174i	$0.0933807\pi$
$467$	15.7553	+	27.2891i	0.729071	+	1.26279i	−0.228206	+	0.973613i	$0.573286\pi$
$468$		0			0
$469$	4.55516	−	0.233044i	0.210338	−	0.0107610i
$470$		0			0
$471$	−4.06938	−	7.04837i	−0.187507	−	0.324772i
$472$		0			0
$473$	8.01983	−	13.8908i	0.368752	−	0.638698i
$474$		0			0
$475$	−2.84562	−	4.92876i	−0.130566	−	0.226147i
$476$		0			0
$477$	0.994479			0.0455341
$478$		0			0
$479$	7.35357	+	12.7368i	0.335993	+	0.581958i	0.983675	−	0.179953i	$-0.0575947\pi$
$479$	7.35357	+	12.7368i	0.335993	+	0.581958i	−0.647682	+	0.761911i	$0.724261\pi$
$480$		0			0
$481$	13.8710	−	24.0254i	0.632465	−	1.09546i
$482$		0			0
$483$	−2.92979			−0.133310
$484$		0			0
$485$	−3.17186	−	5.49382i	−0.144027	−	0.249462i
$486$		0			0
$487$	−2.22677	−	3.85689i	−0.100905	−	0.174772i	0.811153	−	0.584834i	$-0.198840\pi$
$487$	−2.22677	−	3.85689i	−0.100905	−	0.174772i	−0.912058	+	0.410062i	$0.865507\pi$
$488$		0			0
$489$	2.81656	−	4.87843i	0.127369	−	0.220610i
$490$		0			0
$491$	−20.4401			−0.922449			−0.461225	−	0.887283i	$-0.652590\pi$
$491$	−20.4401			−0.922449			−0.461225	+	0.887283i	$0.652590\pi$
$492$		0			0
$493$	13.1041			0.590180
$494$		0			0
$495$	0.747022	−	1.29388i	0.0335762	−	0.0581556i
$496$		0			0
$497$	−0.714231	−	1.23708i	−0.0320376	−	0.0554908i
$498$		0			0
$499$	21.4899	+	37.2217i	0.962022	+	1.66627i	0.717411	+	0.696650i	$0.245327\pi$
$499$	21.4899	+	37.2217i	0.962022	+	1.66627i	0.244611	+	0.969621i	$0.421340\pi$
$500$		0			0
$501$	−6.27155	+	10.8626i	−0.280192	+	0.485307i
$502$		0			0
$503$	2.08678	−	3.61441i	0.0930450	−	0.161159i	−0.815746	−	0.578410i	$-0.803673\pi$
$503$	2.08678	−	3.61441i	0.0930450	−	0.161159i	0.908791	+	0.417252i	$0.137007\pi$
$504$		0			0
$505$	5.77102	−	9.99569i	0.256807	−	0.444802i
$506$		0			0
$507$	−0.949749	+	1.64501i	−0.0421798	+	0.0730576i
$508$		0			0
$509$	20.5816			0.912263			0.456132	−	0.889912i	$-0.349235\pi$
$509$	20.5816			0.912263			0.456132	+	0.889912i	$0.349235\pi$
$510$		0			0
$511$	−7.01614			−0.310376
$512$		0			0
$513$	2.84562	+	4.92876i	0.125637	+	0.217610i
$514$		0			0
$515$	5.46368	−	9.46337i	0.240759	−	0.417006i
$516$		0			0
$517$	5.61047	+	9.71762i	0.246748	+	0.427381i
$518$		0			0
$519$	−5.39925	−	9.35177i	−0.237001	−	0.410497i
$520$		0			0
$521$	13.8335			0.606058			0.303029	−	0.952981i	$-0.402002\pi$
$521$	13.8335			0.606058			0.303029	+	0.952981i	$0.402002\pi$
$522$		0			0
$523$	−13.2693	−	22.9831i	−0.580225	−	1.00498i	−0.995452	−	0.0952618i	$-0.969631\pi$
$523$	−13.2693	−	22.9831i	−0.580225	−	1.00498i	0.415227	−	0.909718i	$-0.363702\pi$
$524$		0			0
$525$	−0.278615	+	0.482575i	−0.0121597	+	0.0210613i
$526$		0			0
$527$	39.8887			1.73758
$528$		0			0
$529$	−2.32212	+	4.02203i	−0.100962	+	0.174871i
$530$		0			0
$531$	13.7751			0.597787
$532$		0			0
$533$	−23.4841			−1.01721
$534$		0			0
$535$	12.5291			0.541681
$536$		0			0
$537$	−2.17443			−0.0938335
$538$		0			0
$539$	−9.99441			−0.430490
$540$		0			0
$541$	−14.7438			−0.633885			−0.316943	−	0.948445i	$-0.602656\pi$
$541$	−14.7438			−0.633885			−0.316943	+	0.948445i	$0.602656\pi$
$542$		0			0
$543$	12.4845	−	21.6238i	0.535761	−	0.927966i
$544$		0			0
$545$	0.395687			0.0169494
$546$		0			0
$547$	−0.147022	+	0.254649i	−0.00628619	+	0.0108880i	−0.869151	−	0.494546i	$-0.835334\pi$
$547$	−0.147022	+	0.254649i	−0.00628619	+	0.0108880i	0.862865	+	0.505434i	$0.168668\pi$
$548$		0			0
$549$	−1.32946	−	2.30269i	−0.0567400	−	0.0982765i
$550$		0			0
$551$	11.7742			0.501597
$552$		0			0
$553$	2.57940	+	4.46765i	0.109687	+	0.189984i
$554$		0			0
$555$	4.16330	+	7.21105i	0.176722	+	0.306092i
$556$		0			0
$557$	4.05751	−	7.02782i	0.171922	−	0.297778i	−0.767170	−	0.641444i	$-0.778335\pi$
$557$	4.05751	−	7.02782i	0.171922	−	0.297778i	0.939092	+	0.343666i	$0.111669\pi$
$558$		0			0
$559$	17.8843	+	30.9766i	0.756427	+	1.31017i
$560$		0			0
$561$	−9.46342			−0.399546
$562$		0			0
$563$	41.9005			1.76589			0.882947	−	0.469472i	$-0.155556\pi$
$563$	41.9005			1.76589			0.882947	+	0.469472i	$0.155556\pi$
$564$		0			0
$565$	−1.58814	+	2.75075i	−0.0668138	+	0.115725i
$566$		0			0
$567$	0.278615	−	0.482575i	0.0117007	−	0.0202662i
$568$		0			0
$569$	4.19241	−	7.26147i	0.175755	−	0.304417i	−0.764667	−	0.644425i	$-0.777097\pi$
$569$	4.19241	−	7.26147i	0.175755	−	0.304417i	0.940422	+	0.340009i	$0.110430\pi$
$570$		0			0
$571$	−13.7300	+	23.7811i	−0.574583	+	0.995207i	0.421504	+	0.906827i	$0.361502\pi$
$571$	−13.7300	+	23.7811i	−0.574583	+	0.995207i	−0.996087	+	0.0883806i	$0.971831\pi$
$572$		0			0
$573$	−12.9393	−	22.4116i	−0.540548	−	0.936257i
$574$		0			0
$575$	2.62889	+	4.55337i	0.109632	+	0.189889i
$576$		0			0
$577$	4.54020	−	7.86386i	0.189011	−	0.327377i	−0.755910	−	0.654676i	$-0.772805\pi$
$577$	4.54020	−	7.86386i	0.189011	−	0.327377i	0.944921	+	0.327299i	$0.106138\pi$
$578$		0			0
$579$	−21.4833			−0.892815
$580$		0			0
$581$	−1.26464			−0.0524662
$582$		0			0
$583$	−0.742898	+	1.28674i	−0.0307677	+	0.0532912i
$584$		0			0
$585$	1.66587	+	2.88537i	0.0688753	+	0.119295i
$586$		0			0
$587$	0.815464	+	1.41242i	0.0336578	+	0.0582970i	0.882364	−	0.470568i	$-0.155951\pi$
$587$	0.815464	+	1.41242i	0.0336578	+	0.0582970i	−0.848706	+	0.528865i	$0.822618\pi$
$588$		0			0
$589$	35.8404			1.47678
$590$		0			0
$591$	2.02629	−	3.50963i	0.0833503	−	0.144367i
$592$		0			0
$593$	−2.89720	−	5.01810i	−0.118974	−	0.206069i	0.800387	−	0.599483i	$-0.204627\pi$
$593$	−2.89720	−	5.01810i	−0.118974	−	0.206069i	−0.919361	+	0.393414i	$0.871294\pi$
$594$		0			0
$595$	3.52954			0.144697
$596$		0			0
$597$	−10.4217	−	18.0509i	−0.426530	−	0.738772i
$598$		0			0
$599$	−2.24514	+	3.88869i	−0.0917338	+	0.158888i	−0.908241	−	0.418448i	$-0.862574\pi$
$599$	−2.24514	+	3.88869i	−0.0917338	+	0.158888i	0.816507	+	0.577336i	$0.195908\pi$
$600$		0			0
$601$	13.8165	+	23.9308i	0.563585	+	0.976158i	0.997180	+	0.0750498i	$0.0239116\pi$
$601$	13.8165	+	23.9308i	0.563585	+	0.976158i	−0.433595	+	0.901108i	$0.642755\pi$
$602$		0			0
$603$	4.44952	+	6.87035i	0.181198	+	0.279782i
$604$		0			0
$605$	−4.38392	−	7.59316i	−0.178231	−	0.308706i
$606$		0			0
$607$	−5.43318	+	9.41055i	−0.220526	+	0.381962i	−0.954968	−	0.296709i	$-0.904111\pi$
$607$	−5.43318	+	9.41055i	−0.220526	+	0.381962i	0.734442	+	0.678672i	$0.237444\pi$
$608$		0			0
$609$	−0.576404	−	0.998361i	−0.0233571	−	0.0404556i
$610$		0			0
$611$	−25.0229			−1.01232
$612$		0			0
$613$	−21.6349	−	37.4728i	−0.873826	−	1.51351i	−0.858009	−	0.513635i	$-0.828298\pi$
$613$	−21.6349	−	37.4728i	−0.873826	−	1.51351i	−0.0158169	−	0.999875i	$-0.505035\pi$
$614$		0			0
$615$	3.52430	−	6.10426i	0.142113	−	0.246148i
$616$		0			0
$617$	17.4180			0.701222			0.350611	−	0.936521i	$-0.385974\pi$
$617$	17.4180			0.701222			0.350611	+	0.936521i	$0.385974\pi$
$618$		0			0
$619$	−16.8689	−	29.2177i	−0.678017	−	1.17436i	−0.975577	−	0.219657i	$-0.929506\pi$
$619$	−16.8689	−	29.2177i	−0.678017	−	1.17436i	0.297560	−	0.954703i	$-0.403827\pi$
$620$		0			0
$621$	−2.62889	−	4.55337i	−0.105494	−	0.182720i
$622$		0			0
$623$	−1.33210	+	2.30726i	−0.0533694	+	0.0924385i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−8.50297			−0.339576
$628$		0			0
$629$	26.3708	−	45.6755i	1.05147	−	1.82120i
$630$		0			0
$631$	0.813480	+	1.40899i	0.0323841	+	0.0560909i	0.881763	−	0.471692i	$-0.156357\pi$
$631$	0.813480	+	1.40899i	0.0323841	+	0.0560909i	−0.849379	+	0.527783i	$0.823023\pi$
$632$		0			0
$633$	−12.5884	−	21.8038i	−0.500344	−	0.866622i
$634$		0			0
$635$	−2.74734	+	4.75853i	−0.109025	+	0.188836i
$636$		0			0
$637$	11.1438	−	19.3017i	0.441535	−	0.764761i
$638$		0			0
$639$	1.28175	−	2.22006i	0.0507054	−	0.0878244i
$640$		0			0
$641$	11.0764	−	19.1849i	0.437493	−	0.757760i	−0.560003	−	0.828491i	$-0.689200\pi$
$641$	11.0764	−	19.1849i	0.437493	−	0.757760i	0.997495	+	0.0707310i	$0.0225332\pi$
$642$		0			0
$643$	−27.9355			−1.10167			−0.550835	−	0.834614i	$-0.685691\pi$
$643$	−27.9355			−1.10167			−0.550835	+	0.834614i	$0.685691\pi$
$644$		0			0
$645$	−10.7357			−0.422719
$646$		0			0
$647$	0.188445	+	0.326397i	0.00740855	+	0.0128320i	0.869706	−	0.493570i	$-0.164308\pi$
$647$	0.188445	+	0.326397i	0.00740855	+	0.0128320i	−0.862297	+	0.506402i	$0.830975\pi$
$648$		0			0
$649$	−10.2903	+	17.8233i	−0.403929	+	0.699625i
$650$		0			0
$651$	−1.75456	−	3.03899i	−0.0687667	−	0.119107i
$652$		0			0
$653$	−17.4091	−	30.1534i	−0.681271	−	1.18000i	−0.974593	−	0.223982i	$-0.928094\pi$
$653$	−17.4091	−	30.1534i	−0.681271	−	1.18000i	0.293323	−	0.956014i	$-0.405239\pi$
$654$		0			0
$655$	−1.21891			−0.0476267
$656$		0			0
$657$	−6.29556	−	10.9042i	−0.245613	−	0.425415i
$658$		0			0
$659$	20.1964	−	34.9812i	0.786740	−	1.36267i	−0.141214	−	0.989979i	$-0.545101\pi$
$659$	20.1964	−	34.9812i	0.786740	−	1.36267i	0.927954	−	0.372695i	$-0.121566\pi$
$660$		0			0
$661$	−24.3477			−0.947017			−0.473509	−	0.880789i	$-0.657013\pi$
$661$	−24.3477			−0.947017			−0.473509	+	0.880789i	$0.657013\pi$
$662$		0			0
$663$	10.5518	−	18.2762i	0.409797	−	0.709790i
$664$		0			0
$665$	3.17133			0.122979
$666$		0			0
$667$	−10.8774			−0.421175
$668$		0			0
$669$	−15.0596			−0.582239
$670$		0			0
$671$	3.97255			0.153358
$672$		0			0
$673$	20.7958			0.801618			0.400809	−	0.916162i	$-0.368729\pi$
$673$	20.7958			0.801618			0.400809	+	0.916162i	$0.368729\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	−8.72998	+	15.1208i	−0.335520	+	0.581138i	−0.983585	−	0.180447i	$-0.942245\pi$
$677$	−8.72998	+	15.1208i	−0.335520	+	0.581138i	0.648064	+	0.761586i	$0.275579\pi$
$678$		0			0
$679$	3.53491			0.135657
$680$		0			0
$681$	0.542579	−	0.939775i	0.0207917	−	0.0360122i
$682$		0			0
$683$	5.86159	+	10.1526i	0.224288	+	0.388478i	0.956105	−	0.293023i	$-0.0946611\pi$
$683$	5.86159	+	10.1526i	0.224288	+	0.388478i	−0.731818	+	0.681500i	$0.761328\pi$
$684$		0			0
$685$	18.0492			0.689625
$686$		0			0
$687$	2.45444	+	4.25122i	0.0936429	+	0.162194i
$688$		0			0
$689$	−1.65667	−	2.86944i	−0.0631142	−	0.109317i
$690$		0			0
$691$	−22.2241	+	38.4934i	−0.845446	+	1.46436i	0.0397864	+	0.999208i	$0.487332\pi$
$691$	−22.2241	+	38.4934i	−0.845446	+	1.46436i	−0.885233	+	0.465148i	$0.846001\pi$
$692$		0			0
$693$	0.416263	+	0.720988i	0.0158125	+	0.0273881i
$694$		0			0
$695$	6.41888			0.243482
$696$		0			0
$697$	−44.6465			−1.69111
$698$		0			0
$699$	2.29817	−	3.98055i	0.0869247	−	0.150558i
$700$		0			0
$701$	10.1731	−	17.6202i	0.384231	−	0.665507i	−0.607431	−	0.794372i	$-0.707800\pi$
$701$	10.1731	−	17.6202i	0.384231	−	0.665507i	0.991662	+	0.128865i	$0.0411333\pi$
$702$		0			0
$703$	23.6944	−	41.0398i	0.893650	−	1.54785i
$704$		0			0
$705$	3.75522	−	6.50424i	0.141430	−	0.244964i
$706$		0			0
$707$	3.21578	+	5.56989i	0.120942	+	0.209477i
$708$		0			0
$709$	−17.4546	−	30.2323i	−0.655522	−	1.13540i	−0.981763	−	0.190110i	$-0.939115\pi$
$709$	−17.4546	−	30.2323i	−0.655522	−	1.13540i	0.326241	−	0.945287i	$-0.394218\pi$
$710$		0			0
$711$	−4.62898	+	8.01762i	−0.173600	+	0.300684i
$712$		0			0
$713$	−33.1106			−1.24000
$714$		0			0
$715$	−4.97777			−0.186158
$716$		0			0
$717$	−1.37954	+	2.38943i	−0.0515199	+	0.0892350i
$718$		0			0
$719$	5.98961	+	10.3743i	0.223375	+	0.386896i	0.955831	−	0.293918i	$-0.0949593\pi$
$719$	5.98961	+	10.3743i	0.223375	+	0.386896i	−0.732456	+	0.680815i	$0.761626\pi$
$720$		0			0
$721$	3.04452	+	5.27327i	0.113384	+	0.196387i
$722$		0			0
$723$	26.7135			0.993485
$724$		0			0
$725$	−1.03441	+	1.79165i	−0.0384171	+	0.0665403i
$726$		0			0
$727$	−20.2157	−	35.0147i	−0.749760	−	1.29862i	−0.947937	−	0.318457i	$-0.896835\pi$
$727$	−20.2157	−	35.0147i	−0.749760	−	1.29862i	0.198177	−	0.980166i	$-0.436498\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	34.0006	+	58.8908i	1.25756	+	2.17815i
$732$		0			0
$733$	19.8299	−	34.3464i	0.732435	−	1.26861i	−0.223405	−	0.974726i	$-0.571717\pi$
$733$	19.8299	−	34.3464i	0.732435	−	1.26861i	0.955840	−	0.293888i	$-0.0949494\pi$
$734$		0			0
$735$	3.34475	+	5.79327i	0.123373	+	0.213688i
$736$		0			0
$737$	−12.2133	+	0.624839i	−0.449883	+	0.0230163i
$738$		0			0
$739$	16.4172	+	28.4355i	0.603917	+	1.04602i	0.992222	+	0.124484i	$0.0397276\pi$
$739$	16.4172	+	28.4355i	0.603917	+	1.04602i	−0.388304	+	0.921531i	$0.626939\pi$
$740$		0			0
$741$	9.48088	−	16.4214i	0.348289	−	0.603254i
$742$		0			0
$743$	−11.3518	−	19.6619i	−0.416456	−	0.721324i	0.579124	−	0.815240i	$-0.303395\pi$
$743$	−11.3518	−	19.6619i	−0.416456	−	0.721324i	−0.995580	+	0.0939161i	$0.970061\pi$
$744$		0			0
$745$	18.4943			0.677579
$746$		0			0
$747$	−1.13476	−	1.96546i	−0.0415187	−	0.0719125i
$748$		0			0
$749$	−3.49079	+	6.04623i	−0.127551	+	0.220925i
$750$		0			0
$751$	17.8928			0.652917			0.326458	−	0.945212i	$-0.394145\pi$
$751$	17.8928			0.652917			0.326458	+	0.945212i	$0.394145\pi$
$752$		0			0
$753$	−13.6609	−	23.6614i	−0.497831	−	0.862269i
$754$		0			0
$755$	−10.2407	−	17.7374i	−0.372696	−	0.645528i
$756$		0			0
$757$	−17.2227	+	29.8307i	−0.625971	+	1.08421i	0.362381	+	0.932030i	$0.381964\pi$
$757$	−17.2227	+	29.8307i	−0.625971	+	1.08421i	−0.988352	+	0.152184i	$0.951369\pi$
$758$		0			0
$759$	7.85536			0.285131
$760$		0			0
$761$	22.6900			0.822513			0.411256	−	0.911520i	$-0.365090\pi$
$761$	22.6900			0.822513			0.411256	+	0.911520i	$0.365090\pi$
$762$		0			0
$763$	−0.110244	+	0.190948i	−0.00399111	+	0.00691280i
$764$		0			0
$765$	3.16705	+	5.48549i	0.114505	+	0.198328i
$766$		0			0
$767$	−22.9475	−	39.7462i	−0.828585	−	1.43515i
$768$		0			0
$769$	7.51765	−	13.0209i	0.271093	−	0.469547i	−0.698049	−	0.716050i	$-0.745948\pi$
$769$	7.51765	−	13.0209i	0.271093	−	0.469547i	0.969142	+	0.246503i	$0.0792815\pi$
$770$		0			0
$771$	−8.27080	+	14.3255i	−0.297866	+	0.515919i
$772$		0			0
$773$	−7.54774	+	13.0731i	−0.271473	+	0.470205i	−0.969239	−	0.246120i	$-0.920844\pi$
$773$	−7.54774	+	13.0731i	−0.271473	+	0.470205i	0.697766	+	0.716326i	$0.254177\pi$
$774$		0			0
$775$	−3.14873	+	5.45376i	−0.113106	+	0.195905i
$776$		0			0
$777$	−4.63982			−0.166453
$778$		0			0
$779$	−40.1153			−1.43728
$780$		0			0
$781$	1.91500	+	3.31687i	0.0685240	+	0.118687i
$782$		0			0
$783$	1.03441	−	1.79165i	0.0369669	−	0.0640285i
$784$		0			0
$785$	−4.06938	−	7.04837i	−0.145242	−	0.251567i
$786$		0			0
$787$	−19.0126	−	32.9308i	−0.677727	−	1.17386i	−0.975664	−	0.219272i	$-0.929632\pi$
$787$	−19.0126	−	32.9308i	−0.677727	−	1.17386i	0.297937	−	0.954586i	$-0.403701\pi$
$788$		0			0
$789$	−5.76571			−0.205265
$790$		0			0
$791$	−0.884960	−	1.53280i	−0.0314656	−	0.0545000i
$792$		0			0
$793$	−4.42942	+	7.67198i	−0.157293	+	0.272440i
$794$		0			0
$795$	0.994479			0.0352705
$796$		0			0
$797$	−17.4058	+	30.1477i	−0.616545	+	1.06789i	0.373566	+	0.927604i	$0.378135\pi$
$797$	−17.4058	+	30.1477i	−0.616545	+	1.06789i	−0.990111	+	0.140284i	$0.955198\pi$
$798$		0			0
$799$	−47.5719			−1.68297
$800$		0			0
$801$	−4.78115			−0.168934
$802$		0			0
$803$	18.8117			0.663851
$804$		0			0
$805$	−2.92979			−0.103261
$806$		0			0
$807$	14.2969			0.503275
$808$		0			0
$809$	23.0939			0.811939			0.405969	−	0.913887i	$-0.366934\pi$
$809$	23.0939			0.811939			0.405969	+	0.913887i	$0.366934\pi$
$810$		0			0
$811$	−12.4904	+	21.6340i	−0.438598	+	0.759674i	−0.997582	−	0.0695049i	$-0.977858\pi$
$811$	−12.4904	+	21.6340i	−0.438598	+	0.759674i	0.558984	+	0.829179i	$0.311191\pi$
$812$		0			0
$813$	−13.7819			−0.483352
$814$		0			0
$815$	2.81656	−	4.87843i	0.0986598	−	0.170884i
$816$		0			0
$817$	30.5498	+	52.9139i	1.06880	+	1.85122i
$818$		0			0
$819$	−1.85654			−0.0648729
$820$		0			0
$821$	−0.804094	−	1.39273i	−0.0280631	−	0.0486067i	0.851653	−	0.524106i	$-0.175601\pi$
$821$	−0.804094	−	1.39273i	−0.0280631	−	0.0486067i	−0.879716	+	0.475500i	$0.842267\pi$
$822$		0			0
$823$	19.1890	+	33.2364i	0.668888	+	1.15855i	0.978215	+	0.207593i	$0.0665628\pi$
$823$	19.1890	+	33.2364i	0.668888	+	1.15855i	−0.309327	+	0.950956i	$0.600104\pi$
$824$		0			0
$825$	0.747022	−	1.29388i	0.0260080	−	0.0450471i
$826$		0			0
$827$	−10.5833	−	18.3308i	−0.368018	−	0.637426i	0.621238	−	0.783622i	$-0.286630\pi$
$827$	−10.5833	−	18.3308i	−0.368018	−	0.637426i	−0.989256	+	0.146197i	$0.953297\pi$
$828$		0			0
$829$	34.2747			1.19041			0.595205	−	0.803574i	$-0.297071\pi$
$829$	34.2747			1.19041			0.595205	+	0.803574i	$0.297071\pi$
$830$		0			0
$831$	22.6410			0.785408
$832$		0			0
$833$	21.1860	−	36.6952i	0.734050	−	1.27141i
$834$		0			0
$835$	−6.27155	+	10.8626i	−0.217036	+	0.375917i
$836$		0			0
$837$	3.14873	−	5.45376i	0.108836	−	0.188509i
$838$		0			0
$839$	−0.374515	+	0.648680i	−0.0129297	+	0.0223949i	−0.872418	−	0.488761i	$-0.837449\pi$
$839$	−0.374515	+	0.648680i	−0.0129297	+	0.0223949i	0.859488	+	0.511156i	$0.170782\pi$
$840$		0			0
$841$	12.3600	+	21.4081i	0.426206	+	0.738211i
$842$		0			0
$843$	1.05658	+	1.83005i	0.0363905	+	0.0630302i
$844$		0			0
$845$	−0.949749	+	1.64501i	−0.0326724	+	0.0565902i
$846$		0			0
$847$	4.88569			0.167874
$848$		0			0
$849$	5.03860			0.172924
$850$		0			0
$851$	−21.8897	+	37.9141i	−0.750370	+	1.29968i
$852$		0			0
$853$	5.16858	+	8.95224i	0.176969	+	0.306519i	0.940841	−	0.338849i	$-0.110037\pi$
$853$	5.16858	+	8.95224i	0.176969	+	0.306519i	−0.763872	+	0.645368i	$0.776704\pi$
$854$		0			0
$855$	2.84562	+	4.92876i	0.0973182	+	0.168560i
$856$		0			0
$857$	54.7416			1.86994			0.934969	−	0.354730i	$-0.115427\pi$
$857$	54.7416			1.86994			0.934969	+	0.354730i	$0.115427\pi$
$858$		0			0
$859$	11.9903	−	20.7679i	0.409105	−	0.708591i	−0.585685	−	0.810539i	$-0.699174\pi$
$859$	11.9903	−	20.7679i	0.409105	−	0.708591i	0.994790	+	0.101948i	$0.0325076\pi$
$860$		0			0
$861$	1.96384	+	3.40147i	0.0669275	+	0.115922i
$862$		0			0
$863$	54.8392			1.86675			0.933373	−	0.358907i	$-0.116850\pi$
$863$	54.8392			1.86675			0.933373	+	0.358907i	$0.116850\pi$
$864$		0			0
$865$	−5.39925	−	9.35177i	−0.183580	−	0.317970i
$866$		0			0
$867$	11.5604	−	20.0232i	0.392611	−	0.680023i
$868$		0			0
$869$	−6.91590	−	11.9787i	−0.234606	−	0.406349i
$870$		0			0
$871$	12.4112	−	24.2836i	0.420538	−	0.822820i
$872$		0			0
$873$	3.17186	+	5.49382i	0.107351	+	0.185938i
$874$		0			0
$875$	−0.278615	+	0.482575i	−0.00941889	+	0.0163140i
$876$		0			0
$877$	−27.5538	−	47.7247i	−0.930427	−	1.61155i	−0.782592	−	0.622535i	$-0.786103\pi$
$877$	−27.5538	−	47.7247i	−0.930427	−	1.61155i	−0.147836	−	0.989012i	$-0.547231\pi$
$878$		0			0
$879$	−17.3862			−0.586424
$880$		0			0
$881$	−2.92933	−	5.07375i	−0.0986917	−	0.170939i	0.812452	−	0.583029i	$-0.198132\pi$
$881$	−2.92933	−	5.07375i	−0.0986917	−	0.170939i	−0.911143	+	0.412089i	$0.864799\pi$
$882$		0			0
$883$	−11.4605	+	19.8502i	−0.385676	+	0.668011i	−0.991863	−	0.127312i	$-0.959365\pi$
$883$	−11.4605	+	19.8502i	−0.385676	+	0.668011i	0.606187	+	0.795323i	$0.292698\pi$
$884$		0			0
$885$	13.7751			0.463043
$886$		0			0
$887$	16.8247	+	29.1412i	0.564918	+	0.978467i	0.997057	+	0.0766602i	$0.0244257\pi$
$887$	16.8247	+	29.1412i	0.564918	+	0.978467i	−0.432139	+	0.901807i	$0.642241\pi$
$888$		0			0
$889$	−1.53090	−	2.65159i	−0.0513446	−	0.0889315i
$890$		0			0
$891$	−0.747022	+	1.29388i	−0.0250262	+	0.0433466i
$892$		0			0
$893$	−42.7438			−1.43037
$894$		0			0
$895$	−2.17443			−0.0726832
$896$		0			0
$897$	−8.75878	+	15.1707i	−0.292447	+	0.506533i
$898$		0			0
$899$	−6.51416	−	11.2829i	−0.217260	−	0.376304i
$900$		0			0
$901$	−3.14956	−	5.45520i	−0.104927	−	0.181739i
$902$		0			0
$903$	2.99113	−	5.18079i	0.0995386	−	0.172406i
$904$		0			0
$905$	12.4845	−	21.6238i	0.414999	−	0.718799i
$906$		0			0
$907$	21.3481	−	36.9761i	0.708853	−	1.22777i	−0.256430	−	0.966563i	$-0.582546\pi$
$907$	21.3481	−	36.9761i	0.708853	−	1.22777i	0.965283	−	0.261207i	$-0.0841205\pi$
$908$		0			0
$909$	−5.77102	+	9.99569i	−0.191412	+	0.331536i
$910$		0			0
$911$	36.6980			1.21586			0.607930	−	0.793990i	$-0.292000\pi$
$911$	36.6980			1.21586			0.607930	+	0.793990i	$0.292000\pi$
$912$		0			0
$913$	3.39077			0.112218
$914$		0			0
$915$	−1.32946	−	2.30269i	−0.0439506	−	0.0761247i
$916$		0			0
$917$	0.339606	−	0.588214i	0.0112148	−	0.0194245i
$918$		0			0
$919$	6.92085	+	11.9873i	0.228298	+	0.395423i	0.957304	−	0.289084i	$-0.0933507\pi$
$919$	6.92085	+	11.9873i	0.228298	+	0.395423i	−0.729006	+	0.684507i	$0.760017\pi$
$920$		0			0
$921$	0.164247	+	0.284485i	0.00541213	+	0.00937409i
$922$		0			0
$923$	−8.54095			−0.281129
$924$		0			0
$925$	4.16330	+	7.21105i	0.136889	+	0.237098i
$926$		0			0
$927$	−5.46368	+	9.46337i	−0.179451	+	0.310818i
$928$		0			0
$929$	−56.2988			−1.84710			−0.923552	−	0.383473i	$-0.874728\pi$
$929$	−56.2988			−1.84710			−0.923552	+	0.383473i	$0.874728\pi$
$930$		0			0
$931$	19.0358	−	32.9709i	0.623872	−	1.08058i
$932$		0			0
$933$	27.1554			0.889027
$934$		0			0
$935$	−9.46342			−0.309487
$936$		0			0
$937$	−30.0962			−0.983199			−0.491599	−	0.870822i	$-0.663588\pi$
$937$	−30.0962			−0.983199			−0.491599	+	0.870822i	$0.663588\pi$
$938$		0			0
$939$	−6.23667			−0.203526
$940$		0			0
$941$	12.6032			0.410853			0.205426	−	0.978673i	$-0.434142\pi$
$941$	12.6032			0.410853			0.205426	+	0.978673i	$0.434142\pi$
$942$		0			0
$943$	37.0600			1.20684
$944$		0			0
$945$	0.278615	−	0.482575i	0.00906333	−	0.0156981i
$946$		0			0
$947$	6.96711			0.226401			0.113200	−	0.993572i	$-0.463890\pi$
$947$	6.96711			0.226401			0.113200	+	0.993572i	$0.463890\pi$
$948$		0			0
$949$	−20.9752	+	36.3301i	−0.680884	+	1.17932i
$950$		0			0
$951$	−11.8501	−	20.5249i	−0.384265	−	0.665567i
$952$		0			0
$953$	−8.50825			−0.275609			−0.137805	−	0.990459i	$-0.544005\pi$
$953$	−8.50825			−0.275609			−0.137805	+	0.990459i	$0.544005\pi$
$954$		0			0
$955$	−12.9393	−	22.4116i	−0.418707	−	0.725221i
$956$		0			0
$957$	1.54546	+	2.67681i	0.0499575	+	0.0865290i
$958$		0			0
$959$	−5.02877	+	8.71009i	−0.162387	+	0.281263i
$960$		0			0
$961$	−4.32898	−	7.49801i	−0.139644	−	0.241871i
$962$		0			0
$963$	−12.5291			−0.403745
$964$		0			0
$965$	−21.4833			−0.691572
$966$		0			0
$967$	−7.57961	+	13.1283i	−0.243744	+	0.422177i	−0.961778	−	0.273831i	$-0.911709\pi$
$967$	−7.57961	+	13.1283i	−0.243744	+	0.422177i	0.718034	+	0.696008i	$0.245042\pi$
$968$		0			0
$969$	18.0244	−	31.2193i	0.579029	−	1.00291i
$970$		0			0
$971$	26.4851	−	45.8735i	0.849946	−	1.47215i	−0.0313093	−	0.999510i	$-0.509968\pi$
$971$	26.4851	−	45.8735i	0.849946	−	1.47215i	0.881255	−	0.472640i	$-0.156699\pi$
$972$		0			0
$973$	−1.78839	+	3.09759i	−0.0573332	+	0.0993041i
$974$		0			0
$975$	1.66587	+	2.88537i	0.0533506	+	0.0924059i
$976$		0			0
$977$	−27.4818	−	47.5999i	−0.879222	−	1.52286i	−0.852197	−	0.523222i	$-0.824730\pi$
$977$	−27.4818	−	47.5999i	−0.879222	−	1.52286i	−0.0270252	−	0.999635i	$-0.508603\pi$
$978$		0			0
$979$	3.57163	−	6.18624i	0.114150	−	0.197713i
$980$		0			0
$981$	−0.395687			−0.0126333
$982$		0			0
$983$	3.10992			0.0991909			0.0495954	−	0.998769i	$-0.484207\pi$
$983$	3.10992			0.0991909			0.0495954	+	0.998769i	$0.484207\pi$
$984$		0			0
$985$	2.02629	−	3.50963i	0.0645629	−	0.111826i
$986$		0			0
$987$	2.09252	+	3.62435i	0.0666056	+	0.115364i
$988$		0			0
$989$	−28.2231	−	48.8838i	−0.897441	−	1.55441i
$990$		0			0
$991$	15.0729			0.478807			0.239404	−	0.970920i	$-0.423048\pi$
$991$	15.0729			0.478807			0.239404	+	0.970920i	$0.423048\pi$
$992$		0			0
$993$	5.92309	−	10.2591i	0.187964	−	0.325562i
$994$		0			0
$995$	−10.4217	−	18.0509i	−0.330389	−	0.572251i
$996$		0			0
$997$	−46.0716			−1.45910			−0.729552	−	0.683926i	$-0.760271\pi$
$997$	−46.0716			−1.45910			−0.729552	+	0.683926i	$0.760271\pi$
$998$		0			0
$999$	−4.16330	−	7.21105i	−0.131721	−	0.228148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.l.841.6	✓	22
67.29	even	3	inner	4020.2.q.l.3781.6	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.l.841.6	✓	22	1.1	even	1	trivial
4020.2.q.l.3781.6	yes	22	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(0.278615 - 0.482575i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} -1.00000 q^{5} +(0.278615 - 0.482575i) q^{7} +1.00000 q^{9} +(-0.747022 + 1.29388i) q^{11} +(-1.66587 - 2.88537i) q^{13} +1.00000 q^{15} +(-3.16705 - 5.48549i) q^{17} +(-2.84562 - 4.92876i) q^{19} +(-0.278615 + 0.482575i) q^{21} +(2.62889 + 4.55337i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(-1.03441 + 1.79165i) q^{29} +(-3.14873 + 5.45376i) q^{31} +(0.747022 - 1.29388i) q^{33} +(-0.278615 + 0.482575i) q^{35} +(4.16330 + 7.21105i) q^{37} +(1.66587 + 2.88537i) q^{39} +(3.52430 - 6.10426i) q^{41} -10.7357 q^{43} -1.00000 q^{45} +(3.75522 - 6.50424i) q^{47} +(3.34475 + 5.79327i) q^{49} +(3.16705 + 5.48549i) q^{51} +0.994479 q^{53} +(0.747022 - 1.29388i) q^{55} +(2.84562 + 4.92876i) q^{57} +13.7751 q^{59} +(-1.32946 - 2.30269i) q^{61} +(0.278615 - 0.482575i) q^{63} +(1.66587 + 2.88537i) q^{65} +(4.44952 + 6.87035i) q^{67} +(-2.62889 - 4.55337i) q^{69} +(1.28175 - 2.22006i) q^{71} +(-6.29556 - 10.9042i) q^{73} -1.00000 q^{75} +(0.416263 + 0.720988i) q^{77} +(-4.62898 + 8.01762i) q^{79} +1.00000 q^{81} +(-1.13476 - 1.96546i) q^{83} +(3.16705 + 5.48549i) q^{85} +(1.03441 - 1.79165i) q^{87} -4.78115 q^{89} -1.85654 q^{91} +(3.14873 - 5.45376i) q^{93} +(2.84562 + 4.92876i) q^{95} +(3.17186 + 5.49382i) q^{97} +(-0.747022 + 1.29388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9	\( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) \) 22 * q - 22 * q^3 - 22 * q^5 + q^7 + 22 * q^9 - 6 * q^11 - 7 * q^13 + 22 * q^15 + 4 * q^17 + 2 * q^19 - q^21 + 6 * q^23 + 22 * q^25 - 22 * q^27 + 15 * q^29 - 5 * q^31 + 6 * q^33 - q^35 + 2 * q^37 + 7 * q^39 - 6 * q^43 - 22 * q^45 - 7 * q^47 - 16 * q^49 - 4 * q^51 + 8 * q^53 + 6 * q^55 - 2 * q^57 - 6 * q^59 + 8 * q^61 + q^63 + 7 * q^65 - 9 * q^67 - 6 * q^69 + 12 * q^71 - q^73 - 22 * q^75 + 9 * q^77 - 15 * q^79 + 22 * q^81 - q^83 - 4 * q^85 - 15 * q^87 + 20 * q^89 + 18 * q^91 + 5 * q^93 - 2 * q^95 - 16 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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